Problem: Given $ m \angle BOC = 6x - 73$, and $ m \angle AOB = 8x + 43$, find $m\angle AOB$. $O$ $A$ $C$ $B$
Explanation: From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Since $\angle AOC$ is a straight angle, we know ${m\angle AOC = 180}$ Substitute in the expressions that were given for each measure: $ {8x + 43} + {6x - 73} = {180}$ Combine like terms: $ 14x - 30 = 180$ Add $30$ to both sides: $ 14x = 210$ Divide both sides by $14$ to find $x$ $ x = 15$ Substitute $15$ for $x$ in the expression that was given for $m\angle AOB$ $ m\angle AOB = 8({15}) + 43$ Simplify: $ {m\angle AOB = 120 + 43}$ So ${m\angle AOB = 163}$.